Simplify \(0.64-83\) to \(-82.36\).
\[\sqrt{\frac{{0.003}^{2}}{-82.36}}\]
Simplify \({0.003}^{2}\) to \(9.0\times {10}^{-6}\).
\[\sqrt{\frac{9.0\times {10}^{-6}}{-82.36}}\]
Simplify \(9.0\times {10}^{-6}\) to \(9\times {10}^{-6}\).
\[\sqrt{\frac{9\times {10}^{-6}}{-82.36}}\]
Move the negative sign to the left.
\[\sqrt{-\frac{9\times {10}^{-6}}{82.36}}\]
Simplify.
\[\sqrt{\frac{9\times {10}^{-6}}{82.36}}\imath \]
Simplify \(\sqrt{\frac{9\times {10}^{-6}}{82.36}}\) to \(\frac{\sqrt{9\times {10}^{-6}}}{\sqrt{82.36}}\).
\[\frac{\sqrt{9\times {10}^{-6}}}{\sqrt{82.36}}\imath \]
Use this rule: \(\sqrt{ab}=\sqrt{a}\sqrt{b}\).
\[\frac{\sqrt{9}\sqrt{{10}^{-6}}}{\sqrt{82.36}}\imath \]
Since \(3\times 3=9\), the square root of \(9\) is \(3\).
\[\frac{3\sqrt{{10}^{-6}}}{\sqrt{82.36}}\imath \]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{3\sqrt{\frac{1}{{10}^{6}}}}{\sqrt{82.36}}\imath \]
Simplify \({10}^{6}\) to \(1000000\).
\[\frac{3\sqrt{\frac{1}{1000000}}}{\sqrt{82.36}}\imath \]
Simplify \(\sqrt{\frac{1}{1000000}}\) to \(\frac{\sqrt{1}}{\sqrt{1000000}}\).
\[\frac{3\times \frac{\sqrt{1}}{\sqrt{1000000}}}{\sqrt{82.36}}\imath \]
Simplify \(\sqrt{1}\) to \(1\).
\[\frac{3\times \frac{1}{\sqrt{1000000}}}{\sqrt{82.36}}\imath \]
Since \(1000\times 1000=1000000\), the square root of \(1000000\) is \(1000\).
\[\frac{3\times \frac{1}{1000}}{\sqrt{82.36}}\imath \]
Simplify \(3\times \frac{1}{1000}\) to \(\frac{3}{1000}\).
\[\frac{\frac{3}{1000}}{\sqrt{82.36}}\imath \]
Simplify \(\sqrt{82.36}\) to \(9.075241\).
\[\frac{\frac{3}{1000}}{9.075241}\imath \]
Simplify \(\frac{\frac{3}{1000}}{9.075241}\) to \(0.000331\).
\[0.000331\imath \]
0.00033056973204095*IM
